alegebra 2 help solve the system by substitution
-x-y-z=-8
-4x+4y+5z=7
2x+2z=4

Question

alegebra 2 help solve the system by substitution 
-x-y-z=-8
-4x+4y+5z=7
2x+2z=4

anonymous · Answer

We need to reduce the second equation to less variables.  so multiply equation 1 by -4 and add it to equation 2 and tell me what you get.

anonymous · Answer

8y+9z=39?

anonymous · Answer

yes, so now we have:

-x-y-z = -8 which we can make into x+y+z = 8 by multiplying by -1.
8y+9z =39 
2x+2z = 4

anonymous · Answer

lets get rid of that 2x in equation 3.  So multiply my revised equation 1 by -2.

anonymous · Answer

and add to equation 3

anonymous · Answer

-2x-2y-2z=-16
-2y=12?

anonymous · Answer

-2y +2z = -12

anonymous · Answer

so we have,

x+y+z =8
8y+9z =39
-2y+2z = -12

anonymous · Answer

ok so is that it or is there more steps to it?

anonymous · Answer

this isn't coming out too nice... is this a basic algebra 2 question?

anonymous · Answer

yes I couldn't figure it out I got confused

anonymous · Answer

Well, the answer is x=3 , y=6 , z=−1, but I went through some pretty complex matrixes to find that.  I might have missed something though.  How were you taught to approach this problem?

anonymous · Answer

im homeschooled and my mom didn't really understand how to do it either she told me just to put it into a graphing calculator

anonymous · Answer

ok i got it

anonymous · Answer

lets start from the beginning again shall we?

-x-y-z=-8
-4x+4y+5z=7
2x+2z=4

anonymous · Answer

reducing equation 3 by a factor of 2 gives us:

-x-y-z=-8
-4x+4y+5z=7
x+z=2

and we can add equations 1 and 3 together to simply get 

-x-y-z=-8
-4x+4y+5z=7
-y = -6

y = 6

anonymous · Answer

now multiply equation 1 by -4 and add it to equation 2:

anonymous · Answer

4x+4y+4z=32
8y+9z=46

anonymous · Answer

whoops... 

it should be 8y+9z=39

now plug the y value we found and solve for z

anonymous · Answer

The main ideal is that you can eliminate unknown factor from 3 to 2 and then from 2 to 1,you will get the final answer.This is the algebra way,when you are in university,you can  use Matrix method to solve the problem.
In the above answer,he used equation 1 to eliminate factor x in eqation 2 and 3,then there are only  two factors in eqation 2 and 3,you can get y and z,then you put y and z into eqation 1,you will get x.